The polynomial generated from the given zeros is: $ P(x) = 4x^4-31x^3+60x^2-23x-10 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 1 $ | $ x-1 $ |
$ 2 $ | $ x-2 $ |
$ 5 $ | $ x-5 $ |
$ -\dfrac{ 1 }{ 4 } $ | $ 4x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-2 \right) \cdot \left( x-5 \right) \cdot \left( 4x+1 \right) = 4x^4-31x^3+60x^2-23x-10 $$